Least squares collocation solution of elliptic problems in general regions

We consider the solution of elliptic problems in general regions by embedding and least squares approximation of overdetermined collocated tensor product of basis functions. The resulting least squares problem will generally be ill-conditioned or even singular, and thus, regularization techniques are required. Large scale problems are solved by either conjugate gradient type methods or by a block Gauss-Seidel approach. Numerical results are presented that show the viability of the new method.